Trump, who plans to visit the island on Tuesday, fired off a series of angry tweets from his private golf club, taking aim at the mayor of San Juan.
The Institutional Revolutionary Party loosened its rules on Wednesday, granting President Enrique Pena Nieto more power to pick his own candidate.
The Trump administration is pressing Mexico to do more to stem the flow of migrants fleeing violence and poverty in the region in its ambitious plan for central America.
The offer came after Mexico’s heroin output increased again in 2016.
Between November 2016 and March, Mexico’s refugee agency, COMAR, received 5,421 asylum applications, up from 2,148 over the same period in 2015 and 2016.